Algorithm for Solving the Nonlinear Pulsar Equation

Ingraham, R. L.

doi:10.1086/152530

Cited by 23 publications

(21 citation statements)

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“…The structure of the magnetic field lines suggests that the dead zone extends all the way up to the light cylinder. Beyond the light cylinder the poloidal magnetic field becomes radial, as expected (Ingraham 1973; Michel 1974). Some magnetic field lines are closing up beyond the light cylinder but they do so within the equatorial current sheet due to the finite artificial resistivity in the numerical scheme – it is easy to see the transition between the dead zone and the current sheet within which the magnetic field lines are highly stretched in the radial direction.…”

Section: Mhd Modelsupporting

confidence: 77%

“…(This property makes the problem somewhat similar to the classical eigenvalue problem in the theory of differential equations.) Ingraham (1973) even proposed an iterative algorithm for finding this function. In the same year Michel (1973) did actually find an exact solution to the pulsar equation in the case of a split‐monopole magnetic field that passed through the singular surface both continuously and smoothly.…”

Section: Introductionmentioning

confidence: 99%

“…The electric current of Michel's (1973) solution has the same sign within the magnetosphere, with the exception of the equatorial current sheet that provides current closure. Further analysis by Ingraham (1973) and Michel (1974) suggested that, if the force‐free solution for an axisymmetric rotating dipole existed, then far beyond the light cylinder it should still closely resemble the split‐monopole one. However, in the near zone the structure of the dipolar magnetosphere was expected to be qualitatively different.…”

Section: Introductionmentioning

confidence: 99%

“…Another important feature of this equation is the mathematical singularity at the light cylinder. It was argued by Ingraham (1973) that the condition of smooth passage through this surface together with the appropriate boundary conditions determine the unique electric current function of the pulsar equation. (This property makes the problem somewhat similar to the classical eigenvalue problem in the theory of differential equations.)…”

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confidence: 99%

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Simulations of the axisymmetric magnetospheres of neutron stars

Komissarov

2006

Monthly Notices of the Royal Astronomical Society

193

190

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In this paper we present the results of time‐dependent simulations of the dipolar axisymmetric magnetospheres of neutron stars carried out within the frameworks of both relativistic magnetohydrodynamics (MHD) and resistive force‐free electrodynamics. The results of force‐free simulations reveal the inability of our numerical method to accommodate the equatorial current sheets of pulsar magnetospheres, and raise a question mark about the robustness of this approach. On the other hand, the MHD approach allows us to make significant progress. We start with a non‐rotating magnetically dominated dipolar magnetosphere and follow its evolution as the stellar rotation is switched on. We find that the time‐dependent solution gradually approaches a steady state that is very close to the stationary solution of the pulsar equation found in 1999 by Contopoulos, Kazanas & Fendt. This result suggests that other stationary solutions that have the Y‐point located well inside the light cylinder are unstable. The role of particle inertia and pressure on the structure and dynamics of MHD magnetospheres is studied in detail, as well as the potential implications of dissipative processes in the equatorial current sheet. We argue that pulsars may have differentially rotating magnetospheres which develop noticeable structural oscillations, and that this may help to explain the nature of the subpulse phenomena.

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Section: Mhd Modelsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Simulations of the axisymmetric magnetospheres of neutron stars

Komissarov

2006

Monthly Notices of the Royal Astronomical Society

193

190

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“…Indeed, in the axisymmetric split‐monopole solution for the aligned rotator (Michel 1973), the Poynting flux is proportional to sin 2 θ, where θ is the polar angle. Such a distribution is a natural feature of axisymmetric MHD flows because in the far zone the magnetic field is almost azimuthal and, thus, must vanish at the symmetry axis (Ingraham 1973; Michel 1974). The situation is less clear for the winds from oblique rotators; however, the results of Bogovalov (1999) suggest that the angular distribution of their Poynting flux may not be all that different after all.…”

Section: Introductionmentioning

confidence: 99%

Synchrotron nebulae created by anisotropic magnetized pulsar winds

Komissarov¹,

Lyubarsky²

2004

Monthly Notices of the Royal Astronomical Society

202

228

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In this paper, we give a detailed description of the first attempt to study the properties of the flow produced by a magnetized pulsar wind within a plerionic nebula via fully relativistic magnetohydrodynamic (MHD) simulations. Following the current theoretical models of pulsar winds, we assume that in the equatorial direction the magnetization of the wind drops to zero but its energy flux reaches a maximum. The results of our 2D axisymmetric simulations reveal complex dynamics of the post‐shock flow, very different from the steady quasi‐radial outflow assumed in earlier analytical models for plerions. The termination shock has the shape of a distorted torus and most of the downstream flow is initially confined to the equatorial plane. Provided the wind magnetization is higher than a certain value, the magnetic hoop stress stops the outflow in the surface layers of the equatorial disc and redirects it into magnetically confined polar jets. The outflow in the inner layers of the equatorial disc continues until it reaches the slowly expanding outer shell and then turns back and forms the vortex flow filling the nebular volume at intermediate latitudes. We simulated the synchrotron images of the nebula taking into account the relativistic beaming effect and the particle energy losses. These images are strikingly similar to the well‐known images of the Crab and other pulsar wind nebulae obtained by Chandra and the Hubble Space Telescope. They exhibit both a system of rings, which makes an impression of an equatorial disc‐like or even a toroidal structure, and well‐collimated polar jets, which appear to originate from the pulsar. A number of fine details of the inner Crab nebula find natural explanation including the bright knot discovered by Hester et al. in 1995 very close to the Crab pulsar.

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